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BackSimple beam - Couple moment Mo at left end II Calculator
Formula
| Deflection (AB) | \( y_{\mathrm{AB}} = \frac{-M_0 x}{6 L E I}\left(2 L^2-3 L x+x^2\right) \) |
| Maximum Deflection | \( y_{\mathrm{MAX}} = \frac{-M_0 L^2}{9 \sqrt{3} E I} \quad \text{at} \quad x = \left(\frac{3-\sqrt{3}}{3}\right) L \) |
| Slope (AB) | \( \theta_{\mathrm{AB}} = \frac{-M_0}{6 L E I}\left(2 L^2-6 L x+3 x^2\right) \) |
| Slope at A | \( \theta_{\mathrm{A}} = \frac{-M_0 L}{3 E I} \) |
| Slope at B | \( \theta_{\mathrm{B}} = \frac{M_0 L}{6 E I} \) |
| Moment (AB) | \( M_{\mathrm{AB}} = \frac{M_0}{L}(L-x) \) |
| Shear (AB) | \( V_{\mathrm{AB}} = \frac{-M_0}{L} \) |
| Reactions | \( R_{\mathrm{A}} = \frac{-M_0}{L} \quad R_{\mathrm{B}} = \frac{M_0}{L} \) |
Definitions
| Symbol | Physical quantity | Units |
|---|---|---|
| E·I | Flexural rigidity | N·m², Pa·m⁴ |
| y | Deflection or deformation | m |
| θ | Slope, Angle of rotation | - |
| x | Distance from support (origin) | m |
| L | Length of beam (without overhang) | m |
| M | Moment, Bending moment, Couple moment applied | N·m |
| P | Concentrated load, Point load, Concentrated force | N |
| w | Distributed load, Load per unit length | N/m |
| R | Reaction load, reaction force | N |
| V | Shear force, shear | N |